Hi. It's Mr. Andersen and this AP Physics essentials video 30. It is on the electric
field of parallel plates. And we have already learned so far that the electric field will
look like this. It will go from the positive to the negative. But we have not gotten into
the details of that. Before we get there let me give you a quick application of this. In
biology we use gel electrophoresis. And what you do is create an electric field across
this gel. And then you can add DNA fragments to it. So we are going to put DNA fragments
in right here. And what happens is they will respond to that electric field. And DNA has
a negative charge and so what they are going to do is they are going to migrate across
that electric field. Now what is interesting is the DNA is each going to have a different
size. And so the small fragments will be able to move really, really far. And the larger
fragments will not move this far. And so we can create a DNA fingerprint. And so if we
have two parallel plates and we make sure they are oppositely charged and we also make
sure that charge is uniformly distributed and we also make sure that we are really far
from the edge, as long as those three things are true, then we can represent the electric
field like this. And if that is our electric field, we know that the electric field strength
is going to act perpendicular to those plates. And it is also going to be constant or uniform
throughout. In other words no matter where you test the electric field inside here, it
is going to give you the same value. It is going to be the same direction and it is always
going to be the same size. Now how do you figure out the electric field strength here?
There are a couple of ways we could do it. We could look at the voltage across that gap.
And then the displacement or r across the gap. And that would tell us the electric field
strength. Or we could just use the charge of the plates and the area of those individual
plates. And that is going to give use the electric field strength as well. The last
thing you should pick up from this video is what happens if we add a charged particle
to this electric field? What happens if I take a proton, for example, and I give it
a velocity in the horizontal right here? Can you predict what is going to happen as it
enters into the electric field? Remember positive charges are going to follow the electric field.
And so watch what happens as we let it go. So it bends like that. But you can see that
it continues to have the same velocity in the horizontal. But what we are really doing
is changing it the vertical. And so this works exactly like projectile motion. However, projectile
motion, that electric field is going to be the gravitational field. So can you predict
what will happen if I take a negative charge and add it in that direction? Which way do
you think it is going to go? Like that. It looks just like throwing a baseball, that
parabolic curve because it is the same thing. It is moving horizontally and that is not
affected by that change in the force in the vertical. So in order to look at the electric
field of parallel plates it is sometimes easier to look at them individually. So if we look
at the positive plate and we draw the electric field lines it is going to look like that.
It is all moving out from the plate. And now if we draw the negative it is going to be
moving towards the plate. And so if I know simply just combine those two, it is going
to look like this. Now you can see on the edge, in order to figure out which way they
are going we would have to do some vector addition. And so we are just going to say
that we are really far from the edge. And then you can also see up here and down here
that that net electric field, since it is so close together in relation to the overall
length of this plate, that it is also a net of zero. The only place where they are going
in the same direction is going to be in the middle. And so we can treat that as our net
electric field. That uniform electric field on the inside. And if we want to figure out
what the electric field strength is, we could use the charge and the area of those plates.
And so if we use this equation, what we have here is the electric field strength is equal
to Q, which is going to be the charge divided by the permittivity of free space. Remember
that is a constant. And so that is going to offer resistance to an electric field. And
then we are going to multiply that times area. And so if we increase the charge on the top
then we are going to increase the electric field strength. And if we decrease the area
then we are going to increase electric field strength. So let me kind of walk you through
that in a PHET simulation. We have here our two plates. And we can add charge to that.
And the charge will show up right here. And then we can measure the electric field down
below. So what we are looking at is what happens when we increase Q. And then what happens
when we increase or change A. And so what we are going to do is put our electric field
sensor right in the middle, so you can see there is no electric field strength. And as
we add charge to it, watch what happens to our electric field. It is getting greater.
And so what we could do is at this point we solve for E. If I add more charge or I add
more of the negative charge, you can see I am increasing that electric field strength.
Now what happens if we change the plate area? As we decrease the plate area you can see
that we are increasing the electric field strength. Because it is in the denominator
we decrease, we increase the electric field strength. If we increase the area what we
are doing is decreasing the electric field strength. And so it is a really nice relationship
between charge and the area of the plates and then the electric field strength. But
we could also go at it in a different direction. We could look at the voltage or the potential
across that gap. And then the distance or the displacement between the two. Now voltage
remember is the amount of work that we would have to do to move a positive charge against
that electric field. So that is going to be the voltage. And then r is going to represent
the displacement or the distance between those two plates. And so here is our equation. Again
if we increase the voltage we are going to increase the electric field. And if we decrease
that displacement we are going to increase the electric field as well. And so we have
another little simulation right here. So what I have done is I have the electric field sensor
in the middle. And now we have a voltmeter. And so now as I add voltage I am increasing
the volts, watch what happens to my electric field. So an increase in the voltage, as we
move it up to 1.5 volts is going to increase that electric field. And we could move it
in the opposite direction and we are going to have the same thing. The more voltage you
have, the more potential difference you have, then the greater that electric field strength
is. But watch what happens when we decrease the distance between the two. So as we make
it closer and closer together we are increasing the electric field. Since r is in the denominator,
by decreasing it we are actually increasing the electric field strength. Last thing you
really have to understand is how motion of particles inside an electric field is similar
to motion of objects on our planet. So imagine I were to roll a ball across a table. And
at the moment it goes off the edge of the table, we take a similar ball and we drop
it from a similar height. You maybe have done this before. Which one is going to hit the
ground first? Well the right answer is they are both going to hit the ground at the same
time. And the reason why is that they are both is a gravitational field. And so even
though this one is moving horizontally, that does not affect the force and therefore the
acceleration in the vertical. They both are going to fall at the same rate. Now charged
particles work the same way inside an electric field. And so if this is our electric field
what happens if we add a positive charge to it? It is going to follow those electric field
lines. But what happens if we shoot a positive, let's say a proton, horizontally into the
electric field? It is just like that ball rolling off of the table. It is going to accelerate
down at the same rate as that one charge did to begin with. Or if we add a negative charge,
and that negative charge we shoot into that electric field like this. It is going to do
not what balls do on our planet. It is going to actually go against the field. That is
what is cool about electromagnetism. It is going to go in that direction. But it is still
following the similar as projectile motion because we have this set electric field. And
so did you learn to create representations of the electric field between parallel plates?
Again we have to be far enough from the edge, and the plates have to be close enough together.
Did you learn to calculate the magnitude and determine the direction of the field? Again
we could use voltage and displacement or separation. Or we can use charge and area. And then finally
did you learn to represent the motion of electrically charged particles inside an electric field?
It is similar to that of projectile motion. I hope so. And I hope that was helpful.